Evaluate the integral. \int_{0}^{1}\int_{0}^{\pi}\int_{0}^{\pi}y*\cos(z)dx dy dz

Brennan Flores

Brennan Flores

Answered question

2021-10-25

Evaluate the integral.
010π0πycos(z)dxdydz

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-10-26Added 97 answers

Step 1
Given that: 010π0πycos(z)dxdydz
Step 2
As the given integral have constant limits.
So, each integral can be evaluated separately.
Thus, 010π0πycos(z)dxdydz=011dx0πydy0πcoszdz
=[x]01[y22]0π[sinz]0π
=[10][π2022][sinπsin0]
=1×π22×0
=0
So, 010π0πycos(z)dxdydz=0

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